Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation
[1] G. W. Zumbusch. Adaptive h-p approximation procedures, graded meshes and anisotropic refinement for numerical quadrature. In F. Brezzi, J. Periaux, R. Glowinski, R. Rannacher, and Y. Kuznetsov, editors, Proceedings of The First European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 95, page 12, 1995. accepted, also as report SC-95-24 ZIB, Berlin.
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A set of adaptive algorithms for quadrature on multi-dimensional polyhedral domains is presented. Several kinds of refinement are discussed, covering local improvement of quadrature order and splitting the domain into sub-domains, resulting in isotropic, graded or anisotropic grids. The algorithms are pure local heuristics using no a priori knowledge or tuning parameters. This approach was motivated by results from finite element theory for optimal approximation results. Numerical experiments show the optimality of pure local greedy-like algorithms for singularity-type functions typically occurring in finite element computations.